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Orthocenter, circumcenter and incenter

Source: China TST 1998, problem 4

May 22, 2005
geometrycircumcircleincentertrigonometrygeometry unsolved

Problem Statement

In acute-angled △ABC\bigtriangleup ABC, HH is the orthocenter, OO is the circumcenter and II is the incenter. Given that ∠C>∠B>∠A\angle C > \angle B > \angle A, prove that II lies within △BOH\bigtriangleup BOH.
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